LMFDB - Embedded newform 896.2.z.a.607.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(31,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			607.3
Character	$\chi$	$=$	896.607
Dual form			896.2.z.a.31.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.665801 + 2.48480i) q^{3} +(3.12401 - 0.837076i) q^{5} +(-1.56215 - 2.13534i) q^{7} +(-3.13287 - 1.80877i) q^{9} +(0.376195 - 1.40398i) q^{11} +(3.11315 - 3.11315i) q^{13} +8.31987i q^{15} +(2.02443 - 1.16881i) q^{17} +(4.40643 - 1.18070i) q^{19} +(6.34599 - 2.45991i) q^{21} +(1.15450 - 1.99965i) q^{23} +(4.72861 - 2.73006i) q^{25} +(1.12329 - 1.12329i) q^{27} +(1.55163 + 1.55163i) q^{29} +(-3.88952 - 6.73685i) q^{31} +(3.23814 + 1.86954i) q^{33} +(-6.66761 - 5.36320i) q^{35} +(-0.272421 - 1.01669i) q^{37} +(5.66282 + 9.80830i) q^{39} -2.77210 q^{41} +(7.12142 + 7.12142i) q^{43} +(-11.3012 - 3.02815i) q^{45} +(-1.42516 + 2.46844i) q^{47} +(-2.11939 + 6.67144i) q^{49} +(1.55638 + 5.80851i) q^{51} +(-11.0925 - 2.97221i) q^{53} -4.70094i q^{55} +11.7352i q^{57} +(3.77383 + 1.01120i) q^{59} +(3.72571 + 13.9045i) q^{61} +(1.03167 + 9.51532i) q^{63} +(7.11957 - 12.3315i) q^{65} +(2.59612 + 0.695627i) q^{67} +(4.20006 + 4.20006i) q^{69} +7.48345 q^{71} +(-5.65210 - 9.78973i) q^{73} +(3.63536 + 13.5673i) q^{75} +(-3.58565 + 1.38991i) q^{77} +(0.706717 + 0.408024i) q^{79} +(-3.38303 - 5.85958i) q^{81} +(2.65285 + 2.65285i) q^{83} +(5.34597 - 5.34597i) q^{85} +(-4.88857 + 2.82241i) q^{87} +(-2.40944 + 4.17328i) q^{89} +(-11.5108 - 1.78445i) q^{91} +(19.3294 - 5.17929i) q^{93} +(12.7774 - 7.37703i) q^{95} +5.86541i q^{97} +(-3.71804 + 3.71804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.665801	+	2.48480i	−0.384400	+	1.43460i	0.454710	+	0.890640i	$0.349743\pi$
$3$	−0.665801	+	2.48480i	−0.384400	+	1.43460i	−0.839110	+	0.543962i	$0.816924\pi$
$4$		0			0
$5$	3.12401	−	0.837076i	1.39710	−	0.374352i	0.519797	−	0.854290i	$-0.326008\pi$
$5$	3.12401	−	0.837076i	1.39710	−	0.374352i	0.877302	+	0.479938i	$0.159341\pi$
$6$		0			0
$7$	−1.56215	−	2.13534i	−0.590436	−	0.807084i
$7$	−1.56215	−	2.13534i	−0.590436	−	0.807084i
$8$		0			0
$9$	−3.13287	−	1.80877i	−1.04429	−	0.602922i
$10$		0			0
$11$	0.376195	−	1.40398i	0.113427	−	0.423315i	−0.885737	−	0.464187i	$-0.846347\pi$
$11$	0.376195	−	1.40398i	0.113427	−	0.423315i	0.999164	+	0.0408713i	$0.0130134\pi$
$12$		0			0
$13$	3.11315	−	3.11315i	0.863433	−	0.863433i	−0.128303	−	0.991735i	$-0.540953\pi$
$13$	3.11315	−	3.11315i	0.863433	−	0.863433i	0.991735	+	0.128303i	$0.0409528\pi$
$14$		0			0
$15$			8.31987i			2.14818i
$16$		0			0
$17$	2.02443	−	1.16881i	0.490997	−	0.283477i	−0.233991	−	0.972239i	$-0.575179\pi$
$17$	2.02443	−	1.16881i	0.490997	−	0.283477i	0.724988	+	0.688761i	$0.241845\pi$
$18$		0			0
$19$	4.40643	−	1.18070i	1.01090	−	0.270871i	0.284897	−	0.958558i	$-0.408041\pi$
$19$	4.40643	−	1.18070i	1.01090	−	0.270871i	0.726007	+	0.687687i	$0.241374\pi$
$20$		0			0
$21$	6.34599	−	2.45991i	1.38481	−	0.536797i
$22$		0			0
$23$	1.15450	−	1.99965i	0.240729	−	0.416955i	−0.720193	−	0.693774i	$-0.755947\pi$
$23$	1.15450	−	1.99965i	0.240729	−	0.416955i	0.960922	+	0.276819i	$0.0892802\pi$
$24$		0			0
$25$	4.72861	−	2.73006i	0.945722	−	0.546013i
$26$		0			0
$27$	1.12329	−	1.12329i	0.216177	−	0.216177i
$28$		0			0
$29$	1.55163	+	1.55163i	0.288130	+	0.288130i	0.836341	−	0.548210i	$-0.184691\pi$
$29$	1.55163	+	1.55163i	0.288130	+	0.288130i	−0.548210	+	0.836341i	$0.684691\pi$
$30$		0			0
$31$	−3.88952	−	6.73685i	−0.698579	−	1.20997i	−0.968959	−	0.247221i	$-0.920483\pi$
$31$	−3.88952	−	6.73685i	−0.698579	−	1.20997i	0.270380	−	0.962754i	$-0.412851\pi$
$32$		0			0
$33$	3.23814	+	1.86954i	0.563687	+	0.325445i
$34$		0			0
$35$	−6.66761	−	5.36320i	−1.12703	−	0.906546i
$36$		0			0
$37$	−0.272421	−	1.01669i	−0.0447857	−	0.167142i	0.939911	−	0.341420i	$-0.110908\pi$
$37$	−0.272421	−	1.01669i	−0.0447857	−	0.167142i	−0.984697	+	0.174277i	$0.944241\pi$
$38$		0			0
$39$	5.66282	+	9.80830i	0.906778	+	1.57058i
$40$		0			0
$41$	−2.77210			−0.432929			−0.216464	−	0.976290i	$-0.569453\pi$
$41$	−2.77210			−0.432929			−0.216464	+	0.976290i	$0.569453\pi$
$42$		0			0
$43$	7.12142	+	7.12142i	1.08601	+	1.08601i	0.995935	+	0.0900717i	$0.0287096\pi$
$43$	7.12142	+	7.12142i	1.08601	+	1.08601i	0.0900717	+	0.995935i	$0.471290\pi$
$44$		0			0
$45$	−11.3012	−	3.02815i	−1.68468	−	0.451410i
$46$		0			0
$47$	−1.42516	+	2.46844i	−0.207880	+	0.360059i	−0.951047	−	0.309047i	$-0.899990\pi$
$47$	−1.42516	+	2.46844i	−0.207880	+	0.360059i	0.743166	+	0.669107i	$0.233323\pi$
$48$		0			0
$49$	−2.11939	+	6.67144i	−0.302770	+	0.953064i
$50$		0			0
$51$	1.55638	+	5.80851i	0.217937	+	0.813354i
$52$		0			0
$53$	−11.0925	−	2.97221i	−1.52367	−	0.408265i	−0.602719	−	0.797954i	$-0.705916\pi$
$53$	−11.0925	−	2.97221i	−1.52367	−	0.408265i	−0.920947	+	0.389689i	$0.872583\pi$
$54$		0			0
$55$		−	4.70094i		−	0.633875i
$56$		0			0
$57$			11.7352i			1.55437i
$58$		0			0
$59$	3.77383	+	1.01120i	0.491311	+	0.131646i	0.495965	−	0.868343i	$-0.334815\pi$
$59$	3.77383	+	1.01120i	0.491311	+	0.131646i	−0.00465348	+	0.999989i	$0.501481\pi$
$60$		0			0
$61$	3.72571	+	13.9045i	0.477028	+	1.78029i	0.613551	+	0.789655i	$0.289741\pi$
$61$	3.72571	+	13.9045i	0.477028	+	1.78029i	−0.136523	+	0.990637i	$0.543593\pi$
$62$		0			0
$63$	1.03167	+	9.51532i	0.129978	+	1.19882i
$64$		0			0
$65$	7.11957	−	12.3315i	0.883074	−	1.52953i
$66$		0			0
$67$	2.59612	+	0.695627i	0.317166	+	0.0849844i	0.413890	−	0.910327i	$-0.364170\pi$
$67$	2.59612	+	0.695627i	0.317166	+	0.0849844i	−0.0967240	+	0.995311i	$0.530836\pi$
$68$		0			0
$69$	4.20006	+	4.20006i	0.505628	+	0.505628i
$70$		0			0
$71$	7.48345			0.888122			0.444061	−	0.895997i	$-0.353537\pi$
$71$	7.48345			0.888122			0.444061	+	0.895997i	$0.353537\pi$
$72$		0			0
$73$	−5.65210	−	9.78973i	−0.661529	−	1.14580i	−0.980214	−	0.197941i	$-0.936575\pi$
$73$	−5.65210	−	9.78973i	−0.661529	−	1.14580i	0.318685	−	0.947861i	$-0.396759\pi$
$74$		0			0
$75$	3.63536	+	13.5673i	0.419775	+	1.56662i
$76$		0			0
$77$	−3.58565	+	1.38991i	−0.408623	+	0.158395i
$78$		0			0
$79$	0.706717	+	0.408024i	0.0795119	+	0.0459062i	0.539229	−	0.842159i	$-0.318716\pi$
$79$	0.706717	+	0.408024i	0.0795119	+	0.0459062i	−0.459717	+	0.888066i	$0.652049\pi$
$80$		0			0
$81$	−3.38303	−	5.85958i	−0.375892	−	0.651065i
$82$		0			0
$83$	2.65285	+	2.65285i	0.291188	+	0.291188i	0.837550	−	0.546361i	$-0.183987\pi$
$83$	2.65285	+	2.65285i	0.291188	+	0.291188i	−0.546361	+	0.837550i	$0.683987\pi$
$84$		0			0
$85$	5.34597	−	5.34597i	0.579852	−	0.579852i
$86$		0			0
$87$	−4.88857	+	2.82241i	−0.524109	+	0.302595i
$88$		0			0
$89$	−2.40944	+	4.17328i	−0.255400	+	0.442367i	−0.965004	−	0.262234i	$-0.915541\pi$
$89$	−2.40944	+	4.17328i	−0.255400	+	0.442367i	0.709604	+	0.704601i	$0.248874\pi$
$90$		0			0
$91$	−11.5108	−	1.78445i	−1.20666	−	0.187061i
$92$		0			0
$93$	19.3294	−	5.17929i	2.00436	−	0.537068i
$94$		0			0
$95$	12.7774	−	7.37703i	1.31093	−	0.756867i
$96$		0			0
$97$			5.86541i			0.595542i	0.954637	+	0.297771i	$0.0962432\pi$
$97$			5.86541i			0.595542i	−0.954637	+	0.297771i	$0.903757\pi$
$98$		0			0
$99$	−3.71804	+	3.71804i	−0.373677	+	0.373677i
$100$		0			0
$101$	−0.373632	+	1.39442i	−0.0371778	+	0.138749i	−0.982020	−	0.188776i	$-0.939548\pi$
$101$	−0.373632	+	1.39442i	−0.0371778	+	0.138749i	0.944842	+	0.327525i	$0.106215\pi$
$102$		0			0
$103$	2.10134	+	1.21321i	0.207051	+	0.119541i	0.599940	−	0.800045i	$-0.295191\pi$
$103$	2.10134	+	1.21321i	0.207051	+	0.119541i	−0.392889	+	0.919586i	$0.628524\pi$
$104$		0			0
$105$	17.7658	−	12.9969i	1.73376	−	1.26836i
$106$		0			0
$107$	−4.34758	+	1.16493i	−0.420297	+	0.112618i	−0.462768	−	0.886480i	$-0.653144\pi$
$107$	−4.34758	+	1.16493i	−0.420297	+	0.112618i	0.0424712	+	0.999098i	$0.486477\pi$
$108$		0			0
$109$	−0.842750	+	3.14518i	−0.0807208	+	0.301254i	−0.994470	−	0.105026i	$-0.966507\pi$
$109$	−0.842750	+	3.14518i	−0.0807208	+	0.301254i	0.913749	+	0.406280i	$0.133174\pi$
$110$		0			0
$111$	2.70765			0.256998
$112$		0			0
$113$	11.5397			1.08556			0.542781	−	0.839875i	$-0.317372\pi$
$113$	11.5397			1.08556			0.542781	+	0.839875i	$0.317372\pi$
$114$		0			0
$115$	1.93280	−	7.21331i	0.180235	−	0.672645i
$116$		0			0
$117$	−15.3841	+	4.12215i	−1.42226	+	0.381093i
$118$		0			0
$119$	−5.65827	−	2.49701i	−0.518693	−	0.228901i
$120$		0			0
$121$	7.69665	+	4.44366i	0.699695	+	0.403969i
$122$		0			0
$123$	1.84566	−	6.88811i	0.166418	−	0.621080i
$124$		0			0
$125$	1.05228	−	1.05228i	0.0941192	−	0.0941192i
$126$		0			0
$127$			4.49210i			0.398610i	0.979938	+	0.199305i	$0.0638684\pi$
$127$			4.49210i			0.398610i	−0.979938	+	0.199305i	$0.936132\pi$
$128$		0			0
$129$	−22.4368	+	12.9539i	−1.97545	+	1.14053i
$130$		0			0
$131$	−13.3612	+	3.58012i	−1.16737	+	0.312796i	−0.789907	−	0.613227i	$-0.789871\pi$
$131$	−13.3612	+	3.58012i	−1.16737	+	0.312796i	−0.377465	+	0.926024i	$0.623204\pi$
$132$		0			0
$133$	−9.40469	−	7.56482i	−0.815490	−	0.655953i
$134$		0			0
$135$	2.56889	−	4.44945i	0.221095	−	0.382947i
$136$		0			0
$137$	−2.18423	+	1.26106i	−0.186611	+	0.107740i	−0.590395	−	0.807114i	$-0.701028\pi$
$137$	−2.18423	+	1.26106i	−0.186611	+	0.107740i	0.403784	+	0.914854i	$0.367695\pi$
$138$		0			0
$139$	6.00381	−	6.00381i	0.509237	−	0.509237i	−0.405055	−	0.914292i	$-0.632748\pi$
$139$	6.00381	−	6.00381i	0.509237	−	0.509237i	0.914292	+	0.405055i	$0.132748\pi$
$140$		0			0
$141$	−5.18472	−	5.18472i	−0.436632	−	0.436632i
$142$		0			0
$143$	−3.19964	−	5.54195i	−0.267568	−	0.463441i
$144$		0			0
$145$	6.14613	+	3.54847i	0.510409	+	0.294685i
$146$		0			0
$147$	−15.1661	−	9.70812i	−1.25088	−	0.800713i
$148$		0			0
$149$	2.19951	+	8.20870i	0.180191	+	0.672483i	0.995609	+	0.0936097i	$0.0298406\pi$
$149$	2.19951	+	8.20870i	0.180191	+	0.672483i	−0.815418	+	0.578873i	$0.803493\pi$
$150$		0			0
$151$	−5.11927	−	8.86683i	−0.416600	−	0.721572i	0.578995	−	0.815331i	$-0.303445\pi$
$151$	−5.11927	−	8.86683i	−0.416600	−	0.721572i	−0.995595	+	0.0937588i	$0.970112\pi$
$152$		0			0
$153$	−8.45639			−0.683659
$154$		0			0
$155$	−17.7902	−	17.7902i	−1.42894	−	1.42894i
$156$		0			0
$157$	−14.1817	−	3.79998i	−1.13183	−	0.303272i	−0.356166	−	0.934423i	$-0.615916\pi$
$157$	−14.1817	−	3.79998i	−1.13183	−	0.303272i	−0.775660	+	0.631151i	$0.782583\pi$
$158$		0			0
$159$	14.7707	−	25.5836i	1.17139	−	2.02892i
$160$		0			0
$161$	−6.07342	+	0.658494i	−0.478653	+	0.0518966i
$162$		0			0
$163$	−5.94974	−	22.2047i	−0.466019	−	1.73921i	−0.653488	−	0.756937i	$-0.726695\pi$
$163$	−5.94974	−	22.2047i	−0.466019	−	1.73921i	0.187468	−	0.982271i	$-0.439972\pi$
$164$		0			0
$165$	11.6809	+	3.12989i	0.909358	+	0.243662i
$166$		0			0
$167$			3.82099i			0.295677i	0.989011	+	0.147839i	$0.0472316\pi$
$167$			3.82099i			0.295677i	−0.989011	+	0.147839i	$0.952768\pi$
$168$		0			0
$169$		−	6.38341i		−	0.491032i
$170$		0			0
$171$	−15.9404	−	4.27121i	−1.21899	−	0.326628i
$172$		0			0
$173$	−2.15162	−	8.02996i	−0.163585	−	0.610506i	−0.998216	−	0.0596981i	$-0.980986\pi$
$173$	−2.15162	−	8.02996i	−0.163585	−	0.610506i	0.834632	−	0.550808i	$-0.185680\pi$
$174$		0			0
$175$	−13.2164	−	5.83245i	−0.999067	−	0.440892i
$176$		0			0
$177$	−5.02524	+	8.70397i	−0.377720	+	0.654230i
$178$		0			0
$179$	18.6644	+	5.00112i	1.39504	+	0.373801i	0.876563	−	0.481288i	$-0.159831\pi$
$179$	18.6644	+	5.00112i	1.39504	+	0.373801i	0.518482	+	0.855089i	$0.326497\pi$
$180$		0			0
$181$	6.07189	+	6.07189i	0.451320	+	0.451320i	0.895793	−	0.444472i	$-0.146609\pi$
$181$	6.07189	+	6.07189i	0.451320	+	0.451320i	−0.444472	+	0.895793i	$0.646609\pi$
$182$		0			0
$183$	−37.0306			−2.73738
$184$		0			0
$185$	−1.70209	−	2.94810i	−0.125140	−	0.216749i
$186$		0			0
$187$	−0.879398	−	3.28196i	−0.0643080	−	0.240001i
$188$		0			0
$189$	−4.15336	−	0.643867i	−0.302112	−	0.0468344i
$190$		0			0
$191$	−13.1707	−	7.60410i	−0.952997	−	0.550213i	−0.0589865	−	0.998259i	$-0.518787\pi$
$191$	−13.1707	−	7.60410i	−0.952997	−	0.550213i	−0.894011	+	0.448046i	$0.852120\pi$
$192$		0			0
$193$	−11.2397	−	19.4678i	−0.809053	−	1.40132i	−0.913521	−	0.406792i	$-0.866647\pi$
$193$	−11.2397	−	19.4678i	−0.809053	−	1.40132i	0.104468	−	0.994528i	$-0.466686\pi$
$194$		0			0
$195$	25.9010	+	25.9010i	1.85481	+	1.85481i
$196$		0			0
$197$	8.31581	−	8.31581i	0.592477	−	0.592477i	−0.345823	−	0.938300i	$-0.612400\pi$
$197$	8.31581	−	8.31581i	0.592477	−	0.592477i	0.938300	+	0.345823i	$0.112400\pi$
$198$		0			0
$199$	−8.85088	+	5.11006i	−0.627422	+	0.362242i	−0.779753	−	0.626087i	$-0.784655\pi$
$199$	−8.85088	+	5.11006i	−0.627422	+	0.362242i	0.152331	+	0.988330i	$0.451322\pi$
$200$		0			0
$201$	−3.45699	+	5.98769i	−0.243837	+	0.422339i
$202$		0			0
$203$	0.889390	−	5.73713i	0.0624229	−	0.402668i
$204$		0			0
$205$	−8.66006	+	2.32046i	−0.604845	+	0.162068i
$206$		0			0
$207$	−7.23378	+	4.17642i	−0.502782	+	0.290282i
$208$		0			0
$209$		−	6.63070i		−	0.458655i
$210$		0			0
$211$	5.73766	−	5.73766i	0.394997	−	0.394997i	−0.481467	−	0.876464i	$-0.659896\pi$
$211$	5.73766	−	5.73766i	0.394997	−	0.394997i	0.876464	+	0.481467i	$0.159896\pi$
$212$		0			0
$213$	−4.98248	+	18.5949i	−0.341394	+	1.27410i
$214$		0			0
$215$	28.2086	+	16.2862i	1.92381	+	1.11071i
$216$		0			0
$217$	−8.30949	+	18.8294i	−0.564085	+	1.27822i
$218$		0			0
$219$	28.0887	−	7.52635i	1.89806	−	0.508583i
$220$		0			0
$221$	2.66369	−	9.94104i	0.179179	−	0.668706i
$222$		0			0
$223$	−17.4929			−1.17141			−0.585705	−	0.810524i	$-0.699182\pi$
$223$	−17.4929			−1.17141			−0.585705	+	0.810524i	$0.699182\pi$
$224$		0			0
$225$	−19.7522			−1.31681
$226$		0			0
$227$	−4.53614	+	16.9291i	−0.301074	+	1.12362i	0.635198	+	0.772349i	$0.280919\pi$
$227$	−4.53614	+	16.9291i	−0.301074	+	1.12362i	−0.936272	+	0.351275i	$0.885748\pi$
$228$		0			0
$229$	−6.75227	+	1.80926i	−0.446202	+	0.119560i	−0.474922	−	0.880028i	$-0.657524\pi$
$229$	−6.75227	+	1.80926i	−0.446202	+	0.119560i	0.0287195	+	0.999588i	$0.490857\pi$
$230$		0			0
$231$	−1.06634	−	9.83503i	−0.0701597	−	0.647098i
$232$		0			0
$233$	25.0933	+	14.4876i	1.64392	+	0.949116i	0.979422	+	0.201823i	$0.0646866\pi$
$233$	25.0933	+	14.4876i	1.64392	+	0.949116i	0.664495	+	0.747293i	$0.268647\pi$
$234$		0			0
$235$	−2.38593	+	8.90440i	−0.155641	+	0.580859i
$236$		0			0
$237$	−1.48439	+	1.48439i	−0.0964215	+	0.0964215i
$238$		0			0
$239$			13.3587i			0.864105i	0.901848	+	0.432053i	$0.142211\pi$
$239$			13.3587i			0.864105i	−0.901848	+	0.432053i	$0.857789\pi$
$240$		0			0
$241$	10.5510	−	6.09164i	0.679651	−	0.392397i	−0.120072	−	0.992765i	$-0.538313\pi$
$241$	10.5510	−	6.09164i	0.679651	−	0.392397i	0.799724	+	0.600368i	$0.204979\pi$
$242$		0			0
$243$	21.4157	−	5.73831i	1.37381	−	0.368113i
$244$		0			0
$245$	−1.03650	+	22.6157i	−0.0662195	+	1.44487i
$246$		0			0
$247$	10.0422	−	17.3936i	0.638969	−	1.10673i
$248$		0			0
$249$	−8.35808	+	4.82554i	−0.529672	+	0.305806i
$250$		0			0
$251$	−6.68926	+	6.68926i	−0.422223	+	0.422223i	−0.885968	−	0.463746i	$-0.846505\pi$
$251$	−6.68926	+	6.68926i	−0.422223	+	0.422223i	0.463746	+	0.885968i	$0.346505\pi$
$252$		0			0
$253$	−2.37314	−	2.37314i	−0.149198	−	0.149198i
$254$		0			0
$255$	9.72432	+	16.8430i	0.608961	+	1.05475i
$256$		0			0
$257$	3.32837	+	1.92163i	0.207618	+	0.119868i	0.600204	−	0.799847i	$-0.295086\pi$
$257$	3.32837	+	1.92163i	0.207618	+	0.119868i	−0.392586	+	0.919715i	$0.628419\pi$
$258$		0			0
$259$	−1.74542	+	2.16993i	−0.108455	+	0.134833i
$260$		0			0
$261$	−2.05452	−	7.66759i	−0.127172	−	0.474612i
$262$		0			0
$263$	−3.15784	−	5.46953i	−0.194720	−	0.337266i	0.752088	−	0.659062i	$-0.229047\pi$
$263$	−3.15784	−	5.46953i	−0.194720	−	0.337266i	−0.946809	+	0.321797i	$0.895713\pi$
$264$		0			0
$265$	−37.1409			−2.28155
$266$		0			0
$267$	−8.76556	−	8.76556i	−0.536444	−	0.536444i
$268$		0			0
$269$	23.2914	+	6.24090i	1.42010	+	0.380514i	0.885519	−	0.464603i	$-0.153803\pi$
$269$	23.2914	+	6.24090i	1.42010	+	0.380514i	0.534580	+	0.845118i	$0.320470\pi$
$270$		0			0
$271$	4.73315	−	8.19805i	0.287518	−	0.497996i	−0.685699	−	0.727886i	$-0.740503\pi$
$271$	4.73315	−	8.19805i	0.287518	−	0.497996i	0.973217	+	0.229890i	$0.0738365\pi$
$272$		0			0
$273$	12.0979	−	27.4141i	0.732200	−	1.65918i
$274$		0			0
$275$	−2.05407	−	7.66590i	−0.123865	−	0.462271i
$276$		0			0
$277$	−11.3278	−	3.03526i	−0.680619	−	0.182371i	−0.0980853	−	0.995178i	$-0.531272\pi$
$277$	−11.3278	−	3.03526i	−0.680619	−	0.182371i	−0.582533	+	0.812807i	$0.697938\pi$
$278$		0			0
$279$			28.1409i			1.68475i
$280$		0			0
$281$			5.59517i			0.333780i	0.985976	+	0.166890i	$0.0533724\pi$
$281$			5.59517i			0.333780i	−0.985976	+	0.166890i	$0.946628\pi$
$282$		0			0
$283$	3.70559	+	0.992910i	0.220275	+	0.0590224i	0.367268	−	0.930115i	$-0.380293\pi$
$283$	3.70559	+	0.992910i	0.220275	+	0.0590224i	−0.146994	+	0.989137i	$0.546960\pi$
$284$		0			0
$285$	9.82326	+	36.6609i	0.581880	+	2.17160i
$286$		0			0
$287$	4.33042	+	5.91938i	0.255617	+	0.349410i
$288$		0			0
$289$	−5.76778	+	9.99009i	−0.339281	+	0.587652i
$290$		0			0
$291$	−14.5744	−	3.90519i	−0.854365	−	0.228927i
$292$		0			0
$293$	−9.74731	−	9.74731i	−0.569444	−	0.569444i	0.362529	−	0.931973i	$-0.381913\pi$
$293$	−9.74731	−	9.74731i	−0.569444	−	0.569444i	−0.931973	+	0.362529i	$0.881913\pi$
$294$		0			0
$295$	12.6359			0.735692
$296$		0			0
$297$	−1.15450	−	1.99965i	−0.0669908	−	0.116031i
$298$		0			0
$299$	−2.63108	−	9.81932i	−0.152159	−	0.567866i
$300$		0			0
$301$	4.08198	−	26.3314i	0.235282	−	1.51772i
$302$		0			0
$303$	−3.21608	−	1.85681i	−0.184759	−	0.106671i
$304$		0			0
$305$	23.2783	+	40.3192i	1.33291	+	2.30867i
$306$		0			0
$307$	−20.5735	−	20.5735i	−1.17419	−	1.17419i	−0.981201	−	0.192988i	$-0.938182\pi$
$307$	−20.5735	−	20.5735i	−1.17419	−	1.17419i	−0.192988	−	0.981201i	$-0.561818\pi$
$308$		0			0
$309$	−4.41365	+	4.41365i	−0.251084	+	0.251084i
$310$		0			0
$311$	−0.495271	+	0.285945i	−0.0280843	+	0.0162145i	−0.513976	−	0.857804i	$-0.671828\pi$
$311$	−0.495271	+	0.285945i	−0.0280843	+	0.0162145i	0.485892	+	0.874019i	$0.338495\pi$
$312$		0			0
$313$	0.707287	−	1.22506i	0.0399782	−	0.0692443i	−0.845344	−	0.534222i	$-0.820604\pi$
$313$	0.707287	−	1.22506i	0.0399782	−	0.0692443i	0.885322	+	0.464978i	$0.153938\pi$
$314$		0			0
$315$	11.1880	+	28.8624i	0.630372	+	1.62621i
$316$		0			0
$317$	25.2914	−	6.77681i	1.42051	−	0.380624i	0.534843	−	0.844951i	$-0.320371\pi$
$317$	25.2914	−	6.77681i	1.42051	−	0.380624i	0.885663	+	0.464328i	$0.153704\pi$
$318$		0			0
$319$	2.76217	−	1.59474i	0.154652	−	0.0892882i
$320$		0			0
$321$		−	11.5785i		−	0.646248i
$322$		0			0
$323$	7.54051	−	7.54051i	0.419565	−	0.419565i
$324$		0			0
$325$	6.22177	−	23.2200i	0.345122	−	1.28801i
$326$		0			0
$327$	−7.25406	−	4.18813i	−0.401150	−	0.231604i
$328$		0			0
$329$	7.49728	−	0.812871i	0.413338	−	0.0448150i
$330$		0			0
$331$	2.71378	−	0.727156i	0.149163	−	0.0399681i	−0.183465	−	0.983026i	$-0.558731\pi$
$331$	2.71378	−	0.727156i	0.149163	−	0.0399681i	0.332628	+	0.943058i	$0.392065\pi$
$332$		0			0
$333$	−0.985490	+	3.67790i	−0.0540045	+	0.201548i
$334$		0			0
$335$	8.69259			0.474927
$336$		0			0
$337$	−23.9205			−1.30303			−0.651517	−	0.758634i	$-0.725867\pi$
$337$	−23.9205			−1.30303			−0.651517	+	0.758634i	$0.725867\pi$
$338$		0			0
$339$	−7.68312	+	28.6738i	−0.417290	+	1.55735i
$340$		0			0
$341$	−10.9216	+	2.92644i	−0.591438	+	0.158475i
$342$		0			0
$343$	17.5566	−	5.89614i	0.947969	−	0.318362i
$344$		0			0
$345$	16.6368	+	9.60525i	0.895695	+	0.517130i
$346$		0			0
$347$	−3.23720	+	12.0814i	−0.173782	+	0.648563i	0.822974	+	0.568079i	$0.192313\pi$
$347$	−3.23720	+	12.0814i	−0.173782	+	0.648563i	−0.996756	+	0.0804837i	$0.974353\pi$
$348$		0			0
$349$	−21.9157	+	21.9157i	−1.17312	+	1.17312i	−0.191662	+	0.981461i	$0.561388\pi$
$349$	−21.9157	+	21.9157i	−1.17312	+	1.17312i	−0.981461	+	0.191662i	$0.938612\pi$
$350$		0			0
$351$		−	6.99394i		−	0.373309i
$352$		0			0
$353$	−18.1984	+	10.5069i	−0.968604	+	0.559224i	−0.898810	−	0.438337i	$-0.855567\pi$
$353$	−18.1984	+	10.5069i	−0.968604	+	0.559224i	−0.0697939	+	0.997561i	$0.522234\pi$
$354$		0			0
$355$	23.3784	−	6.26421i	1.24079	−	0.332470i
$356$		0			0
$357$	9.97186	−	12.3972i	0.527767	−	0.656127i
$358$		0			0
$359$	−4.78310	+	8.28458i	−0.252443	+	0.437243i	−0.964198	−	0.265184i	$-0.914567\pi$
$359$	−4.78310	+	8.28458i	−0.252443	+	0.437243i	0.711755	+	0.702428i	$0.247901\pi$
$360$		0			0
$361$	1.56807	−	0.905328i	0.0825302	−	0.0476488i
$362$		0			0
$363$	−16.1661	+	16.1661i	−0.848498	+	0.848498i
$364$		0			0
$365$	−25.8520	−	25.8520i	−1.35315	−	1.35315i
$366$		0			0
$367$	3.06305	+	5.30536i	0.159890	+	0.276938i	0.934829	−	0.355099i	$-0.115553\pi$
$367$	3.06305	+	5.30536i	0.159890	+	0.276938i	−0.774939	+	0.632036i	$0.782219\pi$
$368$		0			0
$369$	8.68463	+	5.01408i	0.452104	+	0.261022i
$370$		0			0
$371$	10.9813	+	28.3292i	0.570123	+	1.47078i
$372$		0			0
$373$	4.25162	+	15.8673i	0.220140	+	0.821575i	0.984293	+	0.176540i	$0.0564906\pi$
$373$	4.25162	+	15.8673i	0.220140	+	0.821575i	−0.764153	+	0.645035i	$0.776843\pi$
$374$		0			0
$375$	1.91411	+	3.31533i	0.0988440	+	0.171203i
$376$		0			0
$377$	9.66091			0.497562
$378$		0			0
$379$	6.05253	+	6.05253i	0.310897	+	0.310897i	0.845257	−	0.534360i	$-0.179447\pi$
$379$	6.05253	+	6.05253i	0.310897	+	0.310897i	−0.534360	+	0.845257i	$0.679447\pi$
$380$		0			0
$381$	−11.1620	−	2.99085i	−0.571846	−	0.153226i
$382$		0			0
$383$	−9.64030	+	16.6975i	−0.492596	+	0.853202i	−0.999964	−	0.00852805i	$-0.997285\pi$
$383$	−9.64030	+	16.6975i	−0.492596	+	0.853202i	0.507367	+	0.861730i	$0.330619\pi$
$384$		0			0
$385$	−10.0381	+	7.34357i	−0.511591	+	0.374263i
$386$		0			0
$387$	−9.42954	−	35.1915i	−0.479330	−	1.78889i
$388$		0			0
$389$	27.6476	+	7.40814i	1.40179	+	0.375608i	0.878986	−	0.476847i	$-0.158221\pi$
$389$	27.6476	+	7.40814i	1.40179	+	0.375608i	0.522801	+	0.852455i	$0.324887\pi$
$390$		0			0
$391$		−	5.39753i		−	0.272965i
$392$		0			0
$393$		−	35.5835i		−	1.79495i
$394$		0			0
$395$	2.54934	+	0.683093i	0.128271	+	0.0343701i
$396$		0			0
$397$	2.40028	+	8.95799i	0.120467	+	0.449588i	0.999638	−	0.0269184i	$-0.00856943\pi$
$397$	2.40028	+	8.95799i	0.120467	+	0.449588i	−0.879171	+	0.476507i	$0.841903\pi$
$398$		0			0
$399$	25.0587	−	18.3321i	1.25451	−	0.917754i
$400$		0			0
$401$	17.5281	−	30.3596i	0.875312	−	1.51609i	0.0188827	−	0.999822i	$-0.493989\pi$
$401$	17.5281	−	30.3596i	0.875312	−	1.51609i	0.856430	−	0.516264i	$-0.172678\pi$
$402$		0			0
$403$	−33.0815	−	8.86416i	−1.64791	−	0.441555i
$404$		0			0
$405$	−15.4735	−	15.4735i	−0.768886	−	0.768886i
$406$		0			0
$407$	−1.52989			−0.0758338
$408$		0			0
$409$	−17.4392	−	30.2056i	−0.862314	−	1.49357i	−0.869690	−	0.493598i	$-0.835681\pi$
$409$	−17.4392	−	30.2056i	−0.862314	−	1.49357i	0.00737621	−	0.999973i	$-0.497652\pi$
$410$		0			0
$411$	−1.67923	−	6.26699i	−0.0828306	−	0.309128i
$412$		0			0
$413$	−3.73603	−	9.63807i	−0.183838	−	0.474258i
$414$		0			0
$415$	10.5082	+	6.06689i	0.515826	+	0.297812i
$416$		0			0
$417$	10.9209	+	18.9156i	0.534801	+	0.926302i
$418$		0			0
$419$	8.57828	+	8.57828i	0.419076	+	0.419076i	0.884885	−	0.465809i	$-0.154237\pi$
$419$	8.57828	+	8.57828i	0.419076	+	0.419076i	−0.465809	+	0.884885i	$0.654237\pi$
$420$		0			0
$421$	7.41183	−	7.41183i	0.361230	−	0.361230i	−0.503035	−	0.864266i	$-0.667783\pi$
$421$	7.41183	−	7.41183i	0.361230	−	0.361230i	0.864266	+	0.503035i	$0.167783\pi$
$422$		0			0
$423$	8.92967	−	5.15555i	0.434175	−	0.250671i
$424$		0			0
$425$	6.38184	−	11.0537i	0.309565	−	0.536182i
$426$		0			0
$427$	23.8709	−	29.6766i	1.15519	−	1.43615i
$428$		0			0
$429$	15.9010	−	4.26065i	0.767706	−	0.205706i
$430$		0			0
$431$	1.39637	−	0.806195i	0.0672608	−	0.0388331i	−0.465992	−	0.884789i	$-0.654303\pi$
$431$	1.39637	−	0.806195i	0.0672608	−	0.0388331i	0.533253	+	0.845956i	$0.320969\pi$
$432$		0			0
$433$			13.0869i			0.628917i	0.949271	+	0.314458i	$0.101823\pi$
$433$			13.0869i			0.628917i	−0.949271	+	0.314458i	$0.898177\pi$
$434$		0			0
$435$	−12.9093	+	12.9093i	−0.618956	+	0.618956i
$436$		0			0
$437$	2.72622	−	10.1744i	0.130413	−	0.486708i
$438$		0			0
$439$	−1.71358	−	0.989334i	−0.0817846	−	0.0472184i	0.458550	−	0.888669i	$-0.348369\pi$
$439$	−1.71358	−	0.989334i	−0.0817846	−	0.0472184i	−0.540335	+	0.841450i	$0.681702\pi$
$440$		0			0
$441$	18.7069	−	17.0673i	0.890803	−	0.812729i
$442$		0			0
$443$	−33.5156	+	8.98048i	−1.59237	+	0.426675i	−0.942728	−	0.333562i	$-0.891749\pi$
$443$	−33.5156	+	8.98048i	−1.59237	+	0.426675i	−0.649646	+	0.760237i	$0.725083\pi$
$444$		0			0
$445$	−4.03377	+	15.0542i	−0.191219	+	0.713640i
$446$		0			0
$447$	−21.8614			−1.03401
$448$		0			0
$449$	20.0460			0.946031			0.473015	−	0.881054i	$-0.343166\pi$
$449$	20.0460			0.946031			0.473015	+	0.881054i	$0.343166\pi$
$450$		0			0
$451$	−1.04285	+	3.89196i	−0.0491058	+	0.183265i
$452$		0			0
$453$	25.4407	−	6.81682i	1.19531	−	0.320282i
$454$		0			0
$455$	−37.4537	+	4.06081i	−1.75586	+	0.190374i
$456$		0			0
$457$	−25.9859	−	15.0030i	−1.21557	−	0.701810i	−0.251603	−	0.967830i	$-0.580958\pi$
$457$	−25.9859	−	15.0030i	−1.21557	−	0.701810i	−0.963967	+	0.266020i	$0.914291\pi$
$458$		0			0
$459$	0.961116	−	3.58693i	0.0448611	−	0.167424i
$460$		0			0
$461$	−18.2334	+	18.2334i	−0.849213	+	0.849213i	−0.990035	−	0.140822i	$-0.955026\pi$
$461$	−18.2334	+	18.2334i	−0.849213	+	0.849213i	0.140822	+	0.990035i	$0.455026\pi$
$462$		0			0
$463$		−	31.3804i		−	1.45837i	−0.684316	−	0.729186i	$-0.739899\pi$
$463$		−	31.3804i		−	1.45837i	0.684316	−	0.729186i	$-0.260101\pi$
$464$		0			0
$465$	56.0497	−	32.3603i	2.59924	−	1.50067i
$466$		0			0
$467$	−23.0310	+	6.17115i	−1.06575	+	0.285567i	−0.748745	−	0.662858i	$-0.769343\pi$
$467$	−23.0310	+	6.17115i	−1.06575	+	0.285567i	−0.317004	+	0.948424i	$0.602677\pi$
$468$		0			0
$469$	−2.57011	−	6.63028i	−0.118677	−	0.306158i
$470$		0			0
$471$	18.8844	−	32.7088i	0.870148	−	1.50714i
$472$		0			0
$473$	12.6774	−	7.31928i	0.582906	−	0.336541i
$474$		0			0
$475$	17.6129	−	17.6129i	0.808135	−	0.808135i
$476$		0			0
$477$	29.3752	+	29.3752i	1.34500	+	1.34500i
$478$		0			0
$479$	17.6784	+	30.6199i	0.807747	+	1.39906i	0.914421	+	0.404764i	$0.132646\pi$
$479$	17.6784	+	30.6199i	0.807747	+	1.39906i	−0.106674	+	0.994294i	$0.534020\pi$
$480$		0			0
$481$	−4.01319	−	2.31701i	−0.182986	−	0.105647i
$482$		0			0
$483$	2.40746	−	15.5297i	0.109543	−	0.706625i
$484$		0			0
$485$	4.90979	+	18.3236i	0.222942	+	0.832032i
$486$		0			0
$487$	−5.31153	−	9.19984i	−0.240688	−	0.416884i	0.720222	−	0.693743i	$-0.244040\pi$
$487$	−5.31153	−	9.19984i	−0.240688	−	0.416884i	−0.960911	+	0.276859i	$0.910706\pi$
$488$		0			0
$489$	59.1357			2.67421
$490$		0			0
$491$	26.9088	+	26.9088i	1.21438	+	1.21438i	0.969572	+	0.244806i	$0.0787243\pi$
$491$	26.9088	+	26.9088i	1.21438	+	1.21438i	0.244806	+	0.969572i	$0.421276\pi$
$492$		0			0
$493$	4.95472	+	1.32761i	0.223149	+	0.0597927i
$494$		0			0
$495$	−8.50291	+	14.7275i	−0.382177	+	0.661950i
$496$		0			0
$497$	−11.6902	−	15.9797i	−0.524379	−	0.716789i
$498$		0			0
$499$	3.28081	+	12.2441i	0.146869	+	0.548123i	0.999665	+	0.0258790i	$0.00823846\pi$
$499$	3.28081	+	12.2441i	0.146869	+	0.548123i	−0.852796	+	0.522244i	$0.825095\pi$
$500$		0			0
$501$	−9.49441	−	2.54402i	−0.424179	−	0.113658i
$502$		0			0
$503$			13.7074i			0.611183i	0.952163	+	0.305591i	$0.0988542\pi$
$503$			13.7074i			0.611183i	−0.952163	+	0.305591i	$0.901146\pi$
$504$		0			0
$505$			4.66892i			0.207764i
$506$		0			0
$507$	15.8615	+	4.25008i	0.704434	+	0.188753i
$508$		0			0
$509$	−6.16734	−	23.0168i	−0.273363	−	1.02020i	−0.956931	−	0.290317i	$-0.906239\pi$
$509$	−6.16734	−	23.0168i	−0.273363	−	1.02020i	0.683568	−	0.729887i	$-0.260427\pi$
$510$		0			0
$511$	−12.0750	+	27.3622i	−0.534168	+	1.21043i
$512$		0			0
$513$	3.62343	−	6.27596i	0.159978	−	0.277091i
$514$		0			0
$515$	7.58014	+	2.03109i	0.334021	+	0.0895007i
$516$		0			0
$517$	2.92950	+	2.92950i	0.128839	+	0.128839i
$518$		0			0
$519$	21.3854			0.938715
$520$		0			0
$521$	11.8589	+	20.5402i	0.519548	+	0.899884i	0.999742	+	0.0227214i	$0.00723308\pi$
$521$	11.8589	+	20.5402i	0.519548	+	0.899884i	−0.480194	+	0.877163i	$0.659434\pi$
$522$		0			0
$523$	4.85978	+	18.1369i	0.212503	+	0.793073i	0.987031	+	0.160532i	$0.0513211\pi$
$523$	4.85978	+	18.1369i	0.212503	+	0.793073i	−0.774527	+	0.632540i	$0.782012\pi$
$524$		0			0
$525$	23.2920	−	28.9569i	1.01655	−	1.26378i
$526$		0			0
$527$	−15.7482	−	9.09220i	−0.686000	−	0.396063i
$528$		0			0
$529$	8.83428	+	15.3014i	0.384099	+	0.665279i
$530$		0			0
$531$	−9.99392	−	9.99392i	−0.433699	−	0.433699i
$532$		0			0
$533$	−8.62996	+	8.62996i	−0.373805	+	0.373805i
$534$		0			0
$535$	−12.6067	+	7.27851i	−0.545037	+	0.314677i
$536$		0			0
$537$	−24.8536	+	43.0476i	−1.07251	+	1.85764i
$538$		0			0
$539$	8.56926	+	5.48534i	0.369104	+	0.236271i
$540$		0			0
$541$	−25.2496	+	6.76561i	−1.08556	+	0.290876i	−0.756874	−	0.653561i	$-0.773274\pi$
$541$	−25.2496	+	6.76561i	−1.08556	+	0.290876i	−0.328691	+	0.944437i	$0.606608\pi$
$542$		0			0
$543$	−19.1301	+	11.0448i	−0.820952	+	0.473977i
$544$		0			0
$545$			10.5310i			0.451100i
$546$		0			0
$547$	−23.8532	+	23.8532i	−1.01989	+	1.01989i	−0.0200929	+	0.999798i	$0.506396\pi$
$547$	−23.8532	+	23.8532i	−1.01989	+	1.01989i	−0.999798	+	0.0200929i	$0.993604\pi$
$548$		0			0
$549$	13.4779	−	50.3001i	0.575221	−	2.14675i
$550$		0			0
$551$	8.66915	+	5.00513i	0.369318	+	0.213226i
$552$		0			0
$553$	−0.232726	−	2.14648i	−0.00989651	−	0.0912775i
$554$		0			0
$555$	8.45871	−	2.26650i	0.359052	−	0.0962077i
$556$		0			0
$557$	−11.1522	+	41.6206i	−0.472534	+	1.76352i	0.158083	+	0.987426i	$0.449468\pi$
$557$	−11.1522	+	41.6206i	−0.472534	+	1.76352i	−0.630617	+	0.776094i	$0.717198\pi$
$558$		0			0
$559$	44.3401			1.87539
$560$		0			0
$561$	8.74052			0.369025
$562$		0			0
$563$	−2.30901	+	8.61735i	−0.0973133	+	0.363178i	−0.997360	−	0.0726153i	$-0.976865\pi$
$563$	−2.30901	+	8.61735i	−0.0973133	+	0.363178i	0.900047	+	0.435793i	$0.143532\pi$
$564$		0			0
$565$	36.0500	−	9.65958i	1.51664	−	0.406382i
$566$		0			0
$567$	−7.22743	+	16.3775i	−0.303524	+	0.687789i
$568$		0			0
$569$	−5.49552	−	3.17284i	−0.230384	−	0.133012i	0.380365	−	0.924836i	$-0.375798\pi$
$569$	−5.49552	−	3.17284i	−0.230384	−	0.133012i	−0.610749	+	0.791824i	$0.709132\pi$
$570$		0			0
$571$	−9.71490	+	36.2565i	−0.406556	+	1.51729i	0.394612	+	0.918848i	$0.370879\pi$
$571$	−9.71490	+	36.2565i	−0.406556	+	1.51729i	−0.801168	+	0.598439i	$0.795788\pi$
$572$		0			0
$573$	27.6637	−	27.6637i	1.15567	−	1.15567i
$574$		0			0
$575$		−	12.6074i		−	0.525765i
$576$		0			0
$577$	−1.63907	+	0.946316i	−0.0682353	+	0.0393957i	−0.533729	−	0.845655i	$-0.679210\pi$
$577$	−1.63907	+	0.946316i	−0.0682353	+	0.0393957i	0.465494	+	0.885051i	$0.345877\pi$
$578$		0			0
$579$	55.8569	−	14.9668i	2.32134	−	0.622000i
$580$		0			0
$581$	1.52061	−	9.80889i	0.0630854	−	0.406941i
$582$		0			0
$583$	−8.34585	+	14.4554i	−0.345650	+	0.598683i
$584$		0			0
$585$	−44.6094	+	25.7553i	−1.84437	+	1.06485i
$586$		0			0
$587$	26.8519	−	26.8519i	1.10830	−	1.10830i	0.114923	−	0.993374i	$-0.463338\pi$
$587$	26.8519	−	26.8519i	1.10830	−	1.10830i	0.993374	−	0.114923i	$-0.0366621\pi$
$588$		0			0
$589$	−25.0931	−	25.0931i	−1.03394	−	1.03394i
$590$		0			0
$591$	15.1265	+	26.1998i	0.622220	+	1.07772i
$592$		0			0
$593$	−23.8885	−	13.7920i	−0.980984	−	0.566372i	−0.0784171	−	0.996921i	$-0.524987\pi$
$593$	−23.8885	−	13.7920i	−0.980984	−	0.566372i	−0.902567	+	0.430549i	$0.858320\pi$
$594$		0			0
$595$	−19.7667	−	3.06430i	−0.810354	−	0.125624i
$596$		0			0
$597$	−6.80456	−	25.3950i	−0.278492	−	1.03935i
$598$		0			0
$599$	11.8101	+	20.4557i	0.482548	+	0.835797i	0.999799	−	0.0200365i	$-0.00637824\pi$
$599$	11.8101	+	20.4557i	0.482548	+	0.835797i	−0.517252	+	0.855833i	$0.673045\pi$
$600$		0			0
$601$	5.61717			0.229129			0.114565	−	0.993416i	$-0.463453\pi$
$601$	5.61717			0.229129			0.114565	+	0.993416i	$0.463453\pi$
$602$		0			0
$603$	−6.87508	−	6.87508i	−0.279975	−	0.279975i
$604$		0			0
$605$	27.7641	+	7.43936i	1.12877	+	0.302453i
$606$		0			0
$607$	2.43281	−	4.21375i	0.0987446	−	0.171031i	−0.812421	−	0.583072i	$-0.801851\pi$
$607$	2.43281	−	4.21375i	0.0987446	−	0.171031i	0.911165	+	0.412041i	$0.135184\pi$
$608$		0			0
$609$	13.6635	+	6.02975i	0.553672	+	0.244338i
$610$		0			0
$611$	3.24791	+	12.1214i	0.131396	+	0.490378i
$612$		0			0
$613$	−3.99109	−	1.06941i	−0.161199	−	0.0431931i	0.177317	−	0.984154i	$-0.443258\pi$
$613$	−3.99109	−	1.06941i	−0.161199	−	0.0431931i	−0.338516	+	0.940961i	$0.609925\pi$
$614$		0			0
$615$		−	23.0635i		−	0.930010i
$616$		0			0
$617$		−	25.3025i		−	1.01864i	−0.860578	−	0.509319i	$-0.829897\pi$
$617$		−	25.3025i		−	1.01864i	0.860578	−	0.509319i	$-0.170103\pi$
$618$		0			0
$619$	−17.7405	−	4.75356i	−0.713051	−	0.191062i	−0.115982	−	0.993251i	$-0.537002\pi$
$619$	−17.7405	−	4.75356i	−0.713051	−	0.191062i	−0.597069	+	0.802190i	$0.703668\pi$
$620$		0			0
$621$	−0.949348	−	3.54302i	−0.0380960	−	0.142176i
$622$		0			0
$623$	12.6753	−	1.37428i	0.507825	−	0.0550595i
$624$		0			0
$625$	−11.2438	+	19.4749i	−0.449753	+	0.778995i
$626$		0			0
$627$	16.4760	+	4.41472i	0.657987	+	0.176307i
$628$		0			0
$629$	−1.73981	−	1.73981i	−0.0693707	−	0.0693707i
$630$		0			0
$631$	41.4293			1.64928			0.824638	−	0.565661i	$-0.191379\pi$
$631$	41.4293			1.64928			0.824638	+	0.565661i	$0.191379\pi$
$632$		0			0
$633$	10.4368	+	18.0771i	0.414826	+	0.718500i
$634$		0			0
$635$	3.76023	+	14.0334i	0.149220	+	0.556897i
$636$		0			0
$637$	14.1712	+	27.3672i	0.561484	+	1.08433i
$638$		0			0
$639$	−23.4447	−	13.5358i	−0.927458	−	0.535468i
$640$		0			0
$641$	−17.0933	−	29.6065i	−0.675146	−	1.16939i	−0.976426	−	0.215852i	$-0.930747\pi$
$641$	−17.0933	−	29.6065i	−0.675146	−	1.16939i	0.301280	−	0.953536i	$-0.402586\pi$
$642$		0			0
$643$	−3.46526	−	3.46526i	−0.136657	−	0.136657i	0.635469	−	0.772126i	$-0.280807\pi$
$643$	−3.46526	−	3.46526i	−0.136657	−	0.136657i	−0.772126	+	0.635469i	$0.780807\pi$
$644$		0			0
$645$	−59.2493	+	59.2493i	−2.33294	+	2.33294i
$646$		0			0
$647$	−27.2890	+	15.7553i	−1.07284	+	0.619406i	−0.928957	−	0.370188i	$-0.879293\pi$
$647$	−27.2890	+	15.7553i	−1.07284	+	0.619406i	−0.143886	+	0.989594i	$0.545960\pi$
$648$		0			0
$649$	2.83939	−	4.91797i	0.111456	−	0.193047i
$650$		0			0
$651$	−41.2549	−	33.1841i	−1.61691	−	1.30059i
$652$		0			0
$653$	−19.3649	+	5.18880i	−0.757805	+	0.203053i	−0.616977	−	0.786981i	$-0.711643\pi$
$653$	−19.3649	+	5.18880i	−0.757805	+	0.203053i	−0.140828	+	0.990034i	$0.544976\pi$
$654$		0			0
$655$	−38.7436	+	22.3686i	−1.51384	+	0.874015i
$656$		0			0
$657$			40.8933i			1.59540i
$658$		0			0
$659$	29.3969	−	29.3969i	1.14514	−	1.14514i	0.157643	−	0.987496i	$-0.449610\pi$
$659$	29.3969	−	29.3969i	1.14514	−	1.14514i	0.987496	−	0.157643i	$-0.0503896\pi$
$660$		0			0
$661$	−12.5518	+	46.8440i	−0.488208	+	1.82202i	0.0769483	+	0.997035i	$0.475482\pi$
$661$	−12.5518	+	46.8440i	−0.488208	+	1.82202i	−0.565157	+	0.824984i	$0.691184\pi$
$662$		0			0
$663$	22.9280	+	13.2375i	0.890450	+	0.514102i
$664$		0			0
$665$	−35.7127	−	15.7601i	−1.38488	−	0.611151i
$666$		0			0
$667$	4.89406	−	1.31136i	0.189499	−	0.0507760i
$668$		0			0
$669$	11.6468	−	43.4664i	0.450290	−	1.68051i
$670$		0			0
$671$	20.9232			0.807733
$672$		0			0
$673$	11.6457			0.448909			0.224454	−	0.974485i	$-0.427940\pi$
$673$	11.6457			0.448909			0.224454	+	0.974485i	$0.427940\pi$
$674$		0			0
$675$	2.24495	−	8.37826i	0.0864080	−	0.322479i
$676$		0			0
$677$	−32.6233	+	8.74138i	−1.25381	+	0.335959i	−0.823809	−	0.566868i	$-0.808155\pi$
$677$	−32.6233	+	8.74138i	−1.25381	+	0.335959i	−0.430006	+	0.902826i	$0.641488\pi$
$678$		0			0
$679$	12.5247	−	9.16263i	0.480653	−	0.351630i
$680$		0			0
$681$	−39.0453	−	22.5428i	−1.49622	−	0.863843i
$682$		0			0
$683$	1.76166	−	6.57460i	0.0674080	−	0.251570i	−0.923997	−	0.382400i	$-0.875098\pi$
$683$	1.76166	−	6.57460i	0.0674080	−	0.251570i	0.991405	+	0.130830i	$0.0417643\pi$
$684$		0			0
$685$	−5.76794	+	5.76794i	−0.220382	+	0.220382i
$686$		0			0
$687$		−	17.9827i		−	0.686081i
$688$		0			0
$689$	−43.7854	+	25.2795i	−1.66809	+	0.963073i
$690$		0			0
$691$	29.7544	−	7.97267i	1.13191	−	0.303295i	0.356217	−	0.934403i	$-0.384066\pi$
$691$	29.7544	−	7.97267i	1.13191	−	0.303295i	0.775695	+	0.631108i	$0.217400\pi$
$692$		0			0
$693$	13.7474	+	2.13117i	0.522221	+	0.0809565i
$694$		0			0
$695$	13.7303	−	23.7816i	0.520821	−	0.902088i
$696$		0			0
$697$	−5.61193	+	3.24005i	−0.212567	+	0.122726i
$698$		0			0
$699$	−52.7060	+	52.7060i	−1.99352	+	1.99352i
$700$		0			0
$701$	28.2191	+	28.2191i	1.06582	+	1.06582i	0.997675	+	0.0681440i	$0.0217077\pi$
$701$	28.2191	+	28.2191i	1.06582	+	1.06582i	0.0681440	+	0.997675i	$0.478292\pi$
$702$		0			0
$703$	−2.40080	−	4.15831i	−0.0905480	−	0.156834i
$704$		0			0
$705$	−20.5371	−	11.8571i	−0.773473	−	0.446565i
$706$		0			0
$707$	3.56123	−	1.38045i	0.133934	−	0.0519171i
$708$		0			0
$709$	4.97862	+	18.5805i	0.186976	+	0.697804i	0.994199	+	0.107557i	$0.0343028\pi$
$709$	4.97862	+	18.5805i	0.186976	+	0.697804i	−0.807223	+	0.590247i	$0.799030\pi$
$710$		0			0
$711$	−1.47604	−	2.55657i	−0.0553557	−	0.0958790i
$712$		0			0
$713$	−17.9618			−0.672673
$714$		0			0
$715$	−14.6347	−	14.6347i	−0.547308	−	0.547308i
$716$		0			0
$717$	−33.1938	−	8.89426i	−1.23965	−	0.332162i
$718$		0			0
$719$	−11.9289	+	20.6615i	−0.444873	+	0.770543i	−0.998043	−	0.0625253i	$-0.980085\pi$
$719$	−11.9289	+	20.6615i	−0.444873	+	0.770543i	0.553170	+	0.833068i	$0.313418\pi$
$720$		0			0
$721$	−0.691981	−	6.38229i	−0.0257707	−	0.237689i
$722$		0			0
$723$	8.11163	+	30.2730i	0.301675	+	1.12587i
$724$		0			0
$725$	11.5731	+	3.10100i	0.429814	+	0.115168i
$726$		0			0
$727$		−	28.5645i		−	1.05940i	−0.848185	−	0.529700i	$-0.822305\pi$
$727$		−	28.5645i		−	1.05940i	0.848185	−	0.529700i	$-0.177695\pi$
$728$		0			0
$729$			36.7360i			1.36059i
$730$		0			0
$731$	22.7404	+	6.09328i	0.841085	+	0.225368i
$732$		0			0
$733$	−6.04445	−	22.5582i	−0.223257	−	0.833206i	−0.983095	−	0.183094i	$-0.941389\pi$
$733$	−6.04445	−	22.5582i	−0.223257	−	0.833206i	0.759839	−	0.650112i	$-0.225278\pi$
$734$		0			0
$735$	−55.5055	−	17.6331i	−2.04735	−	0.650406i
$736$		0			0
$737$	1.95329	−	3.38320i	0.0719504	−	0.124622i
$738$		0			0
$739$	1.72028	+	0.460947i	0.0632814	+	0.0169562i	0.290321	−	0.956929i	$-0.406238\pi$
$739$	1.72028	+	0.460947i	0.0632814	+	0.0169562i	−0.227039	+	0.973886i	$0.572905\pi$
$740$		0			0
$741$	36.5335	+	36.5335i	1.34209	+	1.34209i
$742$		0			0
$743$	−16.7041			−0.612815			−0.306407	−	0.951900i	$-0.599127\pi$
$743$	−16.7041			−0.612815			−0.306407	+	0.951900i	$0.599127\pi$
$744$		0			0
$745$	13.7426	+	23.8029i	0.503490	+	0.872070i
$746$		0			0
$747$	−3.51266	−	13.1094i	−0.128522	−	0.479649i
$748$		0			0
$749$	9.27909	+	7.46379i	0.339051	+	0.272721i
$750$		0			0
$751$	−1.51512	−	0.874754i	−0.0552874	−	0.0319202i	0.472101	−	0.881544i	$-0.343496\pi$
$751$	−1.51512	−	0.874754i	−0.0552874	−	0.0319202i	−0.527389	+	0.849624i	$0.676829\pi$
$752$		0			0
$753$	−12.1678	−	21.0752i	−0.443419	−	0.768024i
$754$		0			0
$755$	−23.4148	−	23.4148i	−0.852153	−	0.852153i
$756$		0			0
$757$	15.6771	−	15.6771i	0.569792	−	0.569792i	−0.362278	−	0.932070i	$-0.618001\pi$
$757$	15.6771	−	15.6771i	0.569792	−	0.569792i	0.932070	+	0.362278i	$0.118001\pi$
$758$		0			0
$759$	7.47683	−	4.31675i	0.271392	−	0.156688i
$760$		0			0
$761$	−25.9814	+	45.0012i	−0.941826	+	1.63129i	−0.179842	+	0.983695i	$0.557559\pi$
$761$	−25.9814	+	45.0012i	−0.941826	+	1.63129i	−0.761984	+	0.647596i	$0.775775\pi$
$762$		0			0
$763$	8.03255	−	3.11368i	0.290798	−	0.112723i
$764$		0			0
$765$	−26.4178	+	7.07864i	−0.955139	+	0.255929i
$766$		0			0
$767$	14.8965	−	8.60050i	0.537882	−	0.310546i
$768$		0			0
$769$		−	34.9699i		−	1.26105i	−0.776170	−	0.630524i	$-0.782840\pi$
$769$		−	34.9699i		−	1.26105i	0.776170	−	0.630524i	$-0.217160\pi$
$770$		0			0
$771$	−6.99090	+	6.99090i	−0.251771	+	0.251771i
$772$		0			0
$773$	3.55817	−	13.2793i	0.127978	−	0.477622i	−0.871950	−	0.489595i	$-0.837145\pi$
$773$	3.55817	−	13.2793i	0.127978	−	0.477622i	0.999928	+	0.0119731i	$0.00381124\pi$
$774$		0			0
$775$	−36.7841	−	21.2373i	−1.32132	−	0.762866i
$776$		0			0
$777$	−4.22974	−	5.78176i	−0.151741	−	0.207419i
$778$		0			0
$779$	−12.2150	+	3.27301i	−0.437650	+	0.117268i
$780$		0			0
$781$	2.81523	−	10.5066i	0.100737	−	0.375956i
$782$		0			0
$783$	3.48586			0.124574
$784$		0			0
$785$	−47.4847			−1.69480
$786$		0			0
$787$	6.42575	−	23.9812i	0.229053	−	0.854838i	−0.751687	−	0.659520i	$-0.770760\pi$
$787$	6.42575	−	23.9812i	0.229053	−	0.854838i	0.980740	−	0.195318i	$-0.0625738\pi$
$788$		0			0
$789$	15.6932	−	4.20498i	0.558692	−	0.149701i
$790$		0			0
$791$	−18.0267	−	24.6412i	−0.640954	−	0.876139i
$792$		0			0
$793$	54.8856	+	31.6882i	1.94904	+	1.12528i
$794$		0			0
$795$	24.7284	−	92.2878i	0.877027	−	3.27311i
$796$		0			0
$797$	13.3302	−	13.3302i	0.472179	−	0.472179i	−0.430440	−	0.902619i	$-0.641642\pi$
$797$	13.3302	−	13.3302i	0.472179	−	0.472179i	0.902619	+	0.430440i	$0.141642\pi$
$798$		0			0
$799$			6.66293i			0.235717i
$800$		0			0
$801$	15.0970	−	8.71624i	0.533425	−	0.307973i
$802$		0			0
$803$	−15.8709	+	4.25258i	−0.560070	+	0.150070i
$804$		0			0
$805$	−18.4222	+	7.14106i	−0.649298	+	0.251689i
$806$		0			0
$807$	−31.0148	+	53.7192i	−1.09177	+	1.89101i
$808$		0			0
$809$	18.7601	−	10.8311i	0.659569	−	0.380803i	−0.132544	−	0.991177i	$-0.542314\pi$
$809$	18.7601	−	10.8311i	0.659569	−	0.380803i	0.792113	+	0.610375i	$0.208981\pi$
$810$		0			0
$811$	−1.51326	+	1.51326i	−0.0531379	+	0.0531379i	−0.733176	−	0.680039i	$-0.761963\pi$
$811$	−1.51326	+	1.51326i	−0.0531379	+	0.0531379i	0.680039	+	0.733176i	$0.261963\pi$
$812$		0			0
$813$	17.2192	+	17.2192i	0.603904	+	0.603904i
$814$		0			0
$815$	−37.1741	−	64.3874i	−1.30215	−	2.25539i
$816$		0			0
$817$	39.7883	+	22.9718i	1.39202	+	0.803681i
$818$		0			0
$819$	32.8344	+	26.4109i	1.14733	+	0.922871i
$820$		0			0
$821$	−12.4214	−	46.3574i	−0.433511	−	1.61788i	−0.744605	−	0.667506i	$-0.767362\pi$
$821$	−12.4214	−	46.3574i	−0.433511	−	1.61788i	0.311094	−	0.950379i	$-0.399305\pi$
$822$		0			0
$823$	15.0408	+	26.0514i	0.524290	+	0.908096i	0.999600	+	0.0282782i	$0.00900244\pi$
$823$	15.0408	+	26.0514i	0.524290	+	0.908096i	−0.475310	+	0.879818i	$0.657664\pi$
$824$		0			0
$825$	20.4158			0.710789
$826$		0			0
$827$	22.5866	+	22.5866i	0.785414	+	0.785414i	0.980739	−	0.195325i	$-0.0625760\pi$
$827$	22.5866	+	22.5866i	0.785414	+	0.785414i	−0.195325	+	0.980739i	$0.562576\pi$
$828$		0			0
$829$	−31.9742	−	8.56747i	−1.11051	−	0.297561i	−0.343473	−	0.939162i	$-0.611603\pi$
$829$	−31.9742	−	8.56747i	−1.11051	−	0.297561i	−0.767038	+	0.641602i	$0.778270\pi$
$830$		0			0
$831$	15.0840	−	26.1263i	0.523260	−	0.906313i
$832$		0			0
$833$	3.50706	+	15.9831i	0.121512	+	0.553780i
$834$		0			0
$835$	3.19846	+	11.9368i	0.110687	+	0.413091i
$836$		0			0
$837$	−11.9365	−	3.19838i	−0.412586	−	0.110552i
$838$		0			0
$839$		−	35.7894i		−	1.23559i	−0.786340	−	0.617794i	$-0.788027\pi$
$839$		−	35.7894i		−	1.23559i	0.786340	−	0.617794i	$-0.211973\pi$
$840$		0			0
$841$		−	24.1849i		−	0.833962i
$842$		0			0
$843$	−13.9029	−	3.72527i	−0.478841	−	0.128305i
$844$		0			0
$845$	−5.34340	−	19.9418i	−0.183818	−	0.686020i
$846$		0			0
$847$	−2.53455	−	23.3766i	−0.0870880	−	0.803231i
$848$		0			0
$849$	−4.93437	+	8.54658i	−0.169347	+	0.293318i
$850$		0			0
$851$	−2.34752	−	0.629017i	−0.0804721	−	0.0215624i
$852$		0			0
$853$	−1.27195	−	1.27195i	−0.0435507	−	0.0435507i	0.684996	−	0.728547i	$-0.259804\pi$
$853$	−1.27195	−	1.27195i	−0.0435507	−	0.0435507i	−0.728547	+	0.684996i	$0.759804\pi$
$854$		0			0
$855$	−53.3733			−1.82533
$856$		0			0
$857$	−17.1377	−	29.6834i	−0.585412	−	1.01396i	−0.994824	−	0.101614i	$-0.967599\pi$
$857$	−17.1377	−	29.6834i	−0.585412	−	1.01396i	0.409411	−	0.912350i	$-0.365734\pi$
$858$		0			0
$859$	−11.5677	−	43.1714i	−0.394686	−	1.47299i	−0.822314	−	0.569034i	$-0.807317\pi$
$859$	−11.5677	−	43.1714i	−0.394686	−	1.47299i	0.427628	−	0.903955i	$-0.359349\pi$
$860$		0			0
$861$	−17.5917	+	6.81912i	−0.599523	+	0.232395i
$862$		0			0
$863$	32.5858	+	18.8134i	1.10923	+	0.640416i	0.938631	−	0.344924i	$-0.112095\pi$
$863$	32.5858	+	18.8134i	1.10923	+	0.640416i	0.170602	+	0.985340i	$0.445429\pi$
$864$		0			0
$865$	−13.4434	−	23.2846i	−0.457088	−	0.791700i
$866$		0			0
$867$	−20.9832	−	20.9832i	−0.712627	−	0.712627i
$868$		0			0
$869$	0.838719	−	0.838719i	0.0284516	−	0.0284516i
$870$		0			0
$871$	10.2477	−	5.91651i	0.347230	−	0.200473i
$872$		0			0
$873$	10.6092	−	18.3756i	0.359065	−	0.621920i
$874$		0			0
$875$	−3.89081	−	0.603167i	−0.131533	−	0.0203908i
$876$		0			0
$877$	20.5119	−	5.49616i	0.692639	−	0.185592i	0.104708	−	0.994503i	$-0.466609\pi$
$877$	20.5119	−	5.49616i	0.692639	−	0.185592i	0.587931	+	0.808911i	$0.299943\pi$
$878$		0			0
$879$	30.7099	−	17.7304i	1.03582	−	0.598031i
$880$		0			0
$881$		−	3.13017i		−	0.105458i	−0.998609	−	0.0527291i	$-0.983208\pi$
$881$		−	3.13017i		−	0.105458i	0.998609	−	0.0527291i	$-0.0167920\pi$
$882$		0			0
$883$	5.90657	−	5.90657i	0.198772	−	0.198772i	−0.600702	−	0.799473i	$-0.705112\pi$
$883$	5.90657	−	5.90657i	0.198772	−	0.198772i	0.799473	+	0.600702i	$0.205112\pi$
$884$		0			0
$885$	−8.41301	+	31.3978i	−0.282800	+	1.05543i
$886$		0			0
$887$	−41.9702	−	24.2315i	−1.40922	−	0.813615i	−0.413908	−	0.910318i	$-0.635837\pi$
$887$	−41.9702	−	24.2315i	−1.40922	−	0.813615i	−0.995313	+	0.0967040i	$0.969170\pi$
$888$		0			0
$889$	9.59219	−	7.01733i	0.321712	−	0.235354i
$890$		0			0
$891$	−9.49940	+	2.54536i	−0.318242	+	0.0852727i
$892$		0			0
$893$	−3.36536	+	12.5597i	−0.112617	+	0.420294i
$894$		0			0
$895$	62.4941			2.08895
$896$		0			0
$897$	26.1508			0.873151
$898$		0			0
$899$	4.41800	−	16.4882i	0.147348	−	0.549912i
$900$		0			0
$901$	−25.9299	+	6.94789i	−0.863849	+	0.231468i
$902$		0			0
$903$	62.7105	+	27.6744i	2.08688	+	0.920946i
$904$		0			0
$905$	24.0513	+	13.8860i	0.799491	+	0.461587i
$906$		0			0
$907$	−9.69974	+	36.1999i	−0.322075	+	1.20200i	0.595146	+	0.803618i	$0.297094\pi$
$907$	−9.69974	+	36.1999i	−0.322075	+	1.20200i	−0.917220	+	0.398381i	$0.869572\pi$
$908$		0			0
$909$	3.69271	−	3.69271i	0.122480	−	0.122480i
$910$		0			0
$911$			12.0871i			0.400463i	0.979749	+	0.200231i	$0.0641694\pi$
$911$			12.0871i			0.400463i	−0.979749	+	0.200231i	$0.935831\pi$
$912$		0			0
$913$	4.72253	−	2.72656i	0.156293	−	0.0902358i
$914$		0			0
$915$	−115.684	+	30.9974i	−3.82439	+	1.02474i
$916$		0			0
$917$	28.5169	+	22.9381i	0.941712	+	0.757481i
$918$		0			0
$919$	−27.6308	+	47.8579i	−0.911455	+	1.57869i	−0.0994447	+	0.995043i	$0.531707\pi$
$919$	−27.6308	+	47.8579i	−0.911455	+	1.57869i	−0.812010	+	0.583643i	$0.801627\pi$
$920$		0			0
$921$	64.8188	−	37.4231i	2.13585	−	1.23313i
$922$		0			0
$923$	23.2971	−	23.2971i	0.766833	−	0.766833i
$924$		0			0
$925$	−4.06379	−	4.06379i	−0.133617	−	0.133617i
$926$		0			0
$927$	−4.38882	−	7.60165i	−0.144148	−	0.249671i
$928$		0			0
$929$	8.64695	+	4.99232i	0.283697	+	0.163793i	0.635096	−	0.772433i	$-0.280961\pi$
$929$	8.64695	+	4.99232i	0.283697	+	0.163793i	−0.351399	+	0.936226i	$0.614294\pi$
$930$		0			0
$931$	−1.46199	+	31.8996i	−0.0479147	+	1.04547i
$932$		0			0
$933$	−0.380765	−	1.42103i	−0.0124657	−	0.0465226i
$934$		0			0
$935$	−5.49450	−	9.51675i	−0.179689	−	0.311231i
$936$		0			0
$937$	−7.92416			−0.258871			−0.129436	−	0.991588i	$-0.541317\pi$
$937$	−7.92416			−0.258871			−0.129436	+	0.991588i	$0.541317\pi$
$938$		0			0
$939$	2.57311	+	2.57311i	0.0839703	+	0.0839703i
$940$		0			0
$941$	−6.10702	−	1.63637i	−0.199083	−	0.0533441i	0.157900	−	0.987455i	$-0.449528\pi$
$941$	−6.10702	−	1.63637i	−0.199083	−	0.0533441i	−0.356983	+	0.934111i	$0.616194\pi$
$942$		0			0
$943$	−3.20038	+	5.54321i	−0.104219	+	0.180512i
$944$		0			0
$945$	−13.5141	+	1.46523i	−0.439613	+	0.0476638i
$946$		0			0
$947$	−2.94453	−	10.9891i	−0.0956843	−	0.357098i	0.901438	−	0.432908i	$-0.142513\pi$
$947$	−2.94453	−	10.9891i	−0.0956843	−	0.357098i	−0.997122	+	0.0758096i	$0.975846\pi$
$948$		0			0
$949$	−48.0727	−	12.8811i	−1.56051	−	0.418137i
$950$		0			0
$951$			67.3561i			2.18417i
$952$		0			0
$953$		−	12.7329i		−	0.412460i	−0.978504	−	0.206230i	$-0.933880\pi$
$953$		−	12.7329i		−	0.412460i	0.978504	−	0.206230i	$-0.0661195\pi$
$954$		0			0
$955$	−47.5105	−	12.7304i	−1.53741	−	0.411946i
$956$		0			0
$957$	2.12356	+	7.92522i	0.0686448	+	0.256186i
$958$		0			0
$959$	6.10489	+	2.69411i	0.197137	+	0.0869974i
$960$		0			0
$961$	−14.7568	+	25.5595i	−0.476025	+	0.824500i
$962$		0			0
$963$	15.7275	+	4.21417i	0.506812	+	0.135800i
$964$		0			0
$965$	−51.4090	−	51.4090i	−1.65491	−	1.65491i
$966$		0			0
$967$	10.6644			0.342944			0.171472	−	0.985189i	$-0.445148\pi$
$967$	10.6644			0.342944			0.171472	+	0.985189i	$0.445148\pi$
$968$		0			0
$969$	13.7162	+	23.7571i	0.440628	+	0.763190i
$970$		0			0
$971$	0.596517	+	2.22623i	0.0191431	+	0.0714431i	0.974837	−	0.222920i	$-0.0715590\pi$
$971$	0.596517	+	2.22623i	0.0191431	+	0.0714431i	−0.955694	+	0.294364i	$0.904892\pi$
$972$		0			0
$973$	−22.1990	−	3.44137i	−0.711669	−	0.110325i
$974$		0			0
$975$	53.5546	+	30.9198i	1.71512	+	0.990225i
$976$		0			0
$977$	7.66274	+	13.2723i	0.245153	+	0.424617i	0.962175	−	0.272434i	$-0.0878286\pi$
$977$	7.66274	+	13.2723i	0.245153	+	0.424617i	−0.717022	+	0.697051i	$0.754495\pi$
$978$		0			0
$979$	4.95277	+	4.95277i	0.158291	+	0.158291i
$980$		0			0
$981$	8.32913	−	8.32913i	0.265929	−	0.265929i
$982$		0			0
$983$	−16.1184	+	9.30595i	−0.514097	+	0.296814i	−0.734516	−	0.678591i	$-0.762591\pi$
$983$	−16.1184	+	9.30595i	−0.514097	+	0.296814i	0.220419	+	0.975405i	$0.429257\pi$
$984$		0			0
$985$	19.0177	−	32.9396i	0.605954	−	1.04954i
$986$		0			0
$987$	−2.97187	+	19.1705i	−0.0945956	+	0.610202i
$988$		0			0
$989$	22.4620	−	6.01867i	0.714249	−	0.191383i
$990$		0			0
$991$	−23.7555	+	13.7153i	−0.754619	+	0.435680i	−0.827361	−	0.561671i	$-0.810159\pi$
$991$	−23.7555	+	13.7153i	−0.754619	+	0.435680i	0.0727413	+	0.997351i	$0.476825\pi$
$992$		0			0
$993$			7.22736i			0.229353i
$994$		0			0
$995$	−23.3727	+	23.3727i	−0.740965	+	0.740965i
$996$		0			0
$997$	−5.02660	+	18.7595i	−0.159194	+	0.594120i	0.839516	+	0.543335i	$0.182839\pi$
$997$	−5.02660	+	18.7595i	−0.159194	+	0.594120i	−0.998710	+	0.0507843i	$0.983828\pi$
$998$		0			0
$999$	−1.44804	−	0.836028i	−0.0458140	−	0.0264507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.a.607.3		56
4.3	odd	2		896.2.z.b.607.12		56
7.3	odd	6	inner	896.2.z.a.479.3		56
8.3	odd	2		112.2.v.a.19.7	yes	56
8.5	even	2		448.2.z.a.47.12		56
16.3	odd	4		448.2.z.a.271.12		56
16.5	even	4		896.2.z.b.159.12		56
16.11	odd	4	inner	896.2.z.a.159.3		56
16.13	even	4		112.2.v.a.75.13	yes	56
28.3	even	6		896.2.z.b.479.12		56
56.3	even	6		112.2.v.a.3.13	✓	56
56.11	odd	6		784.2.w.f.227.13		56
56.19	even	6		784.2.j.a.195.6		56
56.27	even	2		784.2.w.f.19.7		56
56.45	odd	6		448.2.z.a.367.12		56
56.51	odd	6		784.2.j.a.195.5		56
112.3	even	12		448.2.z.a.143.12		56
112.13	odd	4		784.2.w.f.411.13		56
112.45	odd	12		112.2.v.a.59.7	yes	56
112.59	even	12	inner	896.2.z.a.31.3		56
112.61	odd	12		784.2.j.a.587.5		56
112.93	even	12		784.2.j.a.587.6		56
112.101	odd	12		896.2.z.b.31.12		56
112.109	even	12		784.2.w.f.619.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.13	✓	56	56.3	even	6
112.2.v.a.19.7	yes	56	8.3	odd	2
112.2.v.a.59.7	yes	56	112.45	odd	12
112.2.v.a.75.13	yes	56	16.13	even	4
448.2.z.a.47.12		56	8.5	even	2
448.2.z.a.143.12		56	112.3	even	12
448.2.z.a.271.12		56	16.3	odd	4
448.2.z.a.367.12		56	56.45	odd	6
784.2.j.a.195.5		56	56.51	odd	6
784.2.j.a.195.6		56	56.19	even	6
784.2.j.a.587.5		56	112.61	odd	12
784.2.j.a.587.6		56	112.93	even	12
784.2.w.f.19.7		56	56.27	even	2
784.2.w.f.227.13		56	56.11	odd	6
784.2.w.f.411.13		56	112.13	odd	4
784.2.w.f.619.7		56	112.109	even	12
896.2.z.a.31.3		56	112.59	even	12	inner
896.2.z.a.159.3		56	16.11	odd	4	inner
896.2.z.a.479.3		56	7.3	odd	6	inner
896.2.z.a.607.3		56	1.1	even	1	trivial
896.2.z.b.31.12		56	112.101	odd	12
896.2.z.b.159.12		56	16.5	even	4
896.2.z.b.479.12		56	28.3	even	6
896.2.z.b.607.12		56	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.665801 + 2.48480i) q^{3} +(3.12401 - 0.837076i) q^{5} +(-1.56215 - 2.13534i) q^{7} +(-3.13287 - 1.80877i) q^{9} +(0.376195 - 1.40398i) q^{11} +(3.11315 - 3.11315i) q^{13} +8.31987i q^{15} +(2.02443 - 1.16881i) q^{17} +(4.40643 - 1.18070i) q^{19} +(6.34599 - 2.45991i) q^{21} +(1.15450 - 1.99965i) q^{23} +(4.72861 - 2.73006i) q^{25} +(1.12329 - 1.12329i) q^{27} +(1.55163 + 1.55163i) q^{29} +(-3.88952 - 6.73685i) q^{31} +(3.23814 + 1.86954i) q^{33} +(-6.66761 - 5.36320i) q^{35} +(-0.272421 - 1.01669i) q^{37} +(5.66282 + 9.80830i) q^{39} -2.77210 q^{41} +(7.12142 + 7.12142i) q^{43} +(-11.3012 - 3.02815i) q^{45} +(-1.42516 + 2.46844i) q^{47} +(-2.11939 + 6.67144i) q^{49} +(1.55638 + 5.80851i) q^{51} +(-11.0925 - 2.97221i) q^{53} -4.70094i q^{55} +11.7352i q^{57} +(3.77383 + 1.01120i) q^{59} +(3.72571 + 13.9045i) q^{61} +(1.03167 + 9.51532i) q^{63} +(7.11957 - 12.3315i) q^{65} +(2.59612 + 0.695627i) q^{67} +(4.20006 + 4.20006i) q^{69} +7.48345 q^{71} +(-5.65210 - 9.78973i) q^{73} +(3.63536 + 13.5673i) q^{75} +(-3.58565 + 1.38991i) q^{77} +(0.706717 + 0.408024i) q^{79} +(-3.38303 - 5.85958i) q^{81} +(2.65285 + 2.65285i) q^{83} +(5.34597 - 5.34597i) q^{85} +(-4.88857 + 2.82241i) q^{87} +(-2.40944 + 4.17328i) q^{89} +(-11.5108 - 1.78445i) q^{91} +(19.3294 - 5.17929i) q^{93} +(12.7774 - 7.37703i) q^{95} +5.86541i q^{97} +(-3.71804 + 3.71804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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